- #36

#### martinbn

Science Advisor

- 3,326

- 1,655

How is that in contradiction to what I said!As an example, take a Banach space that is not reflexive but still linearly isomorphic to its second continuous dual space.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter GR191511
- Start date

In summary, The gradient of a vector field is a (1,1) tensor and is represented by a smooth section of the tensor product bundle of the tangent bundle and the dual bundle. This gradient can be thought of as a function of the direction vector and is linear in that it factors over linear combinations of vector fields. This formalism can be extended to more general vector bundles by considering connections, which are linear mappings that satisfy the Leibniz rule. f

- #36

Science Advisor

- 3,326

- 1,655

How is that in contradiction to what I said!As an example, take a Banach space that is not reflexive but still linearly isomorphic to its second continuous dual space.

- #37

Science Advisor

Education Advisor

- 1,222

- 796

Is the above a question?How is that in contradiction to what I said!

If yes, then it can be answered by looking up

Share:

- Replies
- 3

- Views
- 478

- Replies
- 4

- Views
- 2K

- Replies
- 7

- Views
- 1K

- Replies
- 7

- Views
- 660

- Replies
- 20

- Views
- 673

- Replies
- 8

- Views
- 1K

- Replies
- 4

- Views
- 290

- Replies
- 3

- Views
- 594

- Replies
- 4

- Views
- 1K

- Replies
- 14

- Views
- 2K